In the dither ring laser gyro (RLG) strapdown inertial navigation system (SINS), gyro outputs are often pre-filtered to eliminate the dither bias, so the distortion of magnitude and phase of filtered data induce the additional attitude algorithm errors. In this paper, the dither demodulation filter was analyzed and its influence on attitude algorithms was researched. The formulas of optimized attitude algorithm were derived to match the response of the filter. The optimization technology did not complex the algorithms because only the algorithms coefficients were amended. The simulations and experiments illustrate that the optimized algorithms can reduce effectively the additional algorithm errors and increase obviously the algorithms precision. The algorithms have great value to real application.